Lesson 4

The addition or subtraction of functions can be used to solve problems that include adding or subtracting values defined by functions. Try This 4 explores a financial example involving adding and subtracting functions.

Try This 4

Suppose that you make two investments, each of $1000. The first investment is in a savings account so that you can access the money if necessary. The second one is in a savings bond that you do not plan to redeem until the bond has matured. The savings account pays an interest rate of 3% per annum, and the bond pays an annual rate of 5%. Assume that the interest is compounded annually and that the value of either investment can be determined for any time, t. Both investments will be removed after 8 yr.

1.  
   1. Give the equation of a function S(t) that represents the value of the savings investment after t years.
   2. Give the equation of a function B(t) that represents the value of the bond investment after t years.
2.  
   1. Give the equation of a function T(t) that represents the total value of the investments after t years.
   2. Give the equation of a function D(t) that represents how much more money is invested in bonds than in the bank account after t years.
3.  
   1. Determine T(6) and D(6). Explain what each value represents.
   2. Determine a time when one investment is worth $100 more than the other.
   3. Determine a time when the investments are worth $2500 together.
4. Determine the domain and range of each of the four functions.

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